Stability and Recurrence of Regime-Switching Diffusion Processes

We provide some criteria on the stability of regime-switching diffusion processes. Both the state-independent and state-dependent regime-switching diffusion processes with switching in a finite state space and an infinite countable state space are studied in this work. We provide two methods to deal...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2014-01, Vol.52 (6), p.3496-3516
Main Authors: Shao, Jinghai, Xi, Fubao
Format: Article
Language:English
Subjects:
Criteria
Diffusion
Eigenvalues
Mathematical analysis
Nonlinearity
Optimization
Stability
Switching
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Summary:We provide some criteria on the stability of regime-switching diffusion processes. Both the state-independent and state-dependent regime-switching diffusion processes with switching in a finite state space and an infinite countable state space are studied in this work. We provide two methods to deal with switching processes in an infinite countable state space. One is a finite partition method based on the nonsingular M-matrix theory. Another is an application of principal eigenvalue of a bilinear form. Our methods can deal with both linear and nonlinear regime-switching diffusion processes. Moreover, the method of principal eigenvalue is also used to study the recurrence of regime-switching diffusion processes.
ISSN:0363-0129
1095-7138
DOI:10.1137/140962905